e) `sin theta -1=?` f) `cos theta +1=?`

Show that ((1 + cos theta - sin ^(2) theta)/( sin theta (1 + cos theta ))) = cot theta

1- (sin ^ (2) theta) / (1 + cos theta) + (1 + cos theta) / (sin theta) - (sin theta) / (1-cos theta) - (1) / (sec theta)

If: cos^(-1) (sin theta) = sin^(-1) (cos theta) , then: theta =

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).

(sin theta-cos theta + 1) / (sin theta + cos theta-1) = (1) / (sec theta-tan theta)

What is ( sin theta - cos theta + 1 )/( sin theta + cos theta -1) - ( sin theta + 1 )/( cos theta ) equal to ?

(1 + sin theta) / (1 + cos theta) + (1-sin theta) / (1-cos theta) =

(1 + sin theta-cos theta) / (1 + sin theta + cos theta) = (tan theta) / (2)